Sr Examen
Integral de 1/(1+sinx-cosx)^2 dx
Solución
Ha introducido
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1 / | | 1 | ---------------------- dx | 2 | (1 + sin(x) - cos(x)) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(\left(\sin{\left(x \right)} + 1\right) - \cos{\left(x \right)}\right)^{2}}\, dx$$
Integral(1/((1 + sin(x) - cos(x))^2), (x, 0, 1))
Respuesta (Indefinida)
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/ /x\ 2/x\ / /x\\ / /x\\ /x\ 2/x\ / /x\\ / /x\\ /x\ | 3*tan|-| 2*tan |-|*log|tan|-|| 2*log|tan|-||*tan|-| 2*tan |-|*log|1 + tan|-|| 2*log|1 + tan|-||*tan|-| | 1 1 \2/ \2/ \ \2// \ \2// \2/ \2/ \ \2// \ \2// \2/ | ---------------------- dx = C - -------------------- - -------------------- - --------------------- - -------------------- + ------------------------- + ------------------------ | 2 2/x\ /x\ 2/x\ /x\ 2/x\ /x\ 2/x\ /x\ 2/x\ /x\ 2/x\ /x\ | (1 + sin(x) - cos(x)) 2*tan |-| + 2*tan|-| 2*tan |-| + 2*tan|-| 2*tan |-| + 2*tan|-| 2*tan |-| + 2*tan|-| 2*tan |-| + 2*tan|-| 2*tan |-| + 2*tan|-| | \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ /
$$\int \frac{1}{\left(\left(\sin{\left(x \right)} + 1\right) - \cos{\left(x \right)}\right)^{2}}\, dx = C + \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{2 \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)}} + \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan{\left(\frac{x}{2} \right)}}{2 \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)}} - \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{2 \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)}} - \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan{\left(\frac{x}{2} \right)}}{2 \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)}} - \frac{3 \tan{\left(\frac{x}{2} \right)}}{2 \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)}} - \frac{1}{2 \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)}}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.